<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title></title>
<!--Generated on Tue Jun  3 20:03:09 2014 by LaTeXML (version 0.7.999_04) http://dlmf.nist.gov/LaTeXML/.-->

<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link rel="stylesheet" href="../../../../../../../LaTeXML.css" type="text/css">
<link rel="stylesheet" href="../../../../../../../ltx-article.css" type="text/css">
<link rel="stylesheet" href="../../../../../../../customRules.css" type="text/css">
</head>
<body>
<div class="ltx_page_main">
<div class="ltx_page_content">
<div class="ltx_document">
<div id="Sx1" class="ltx_section">
<h1 class="ltx_title ltx_title_section">Sub-pixel 2D localization of molecules</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">Sub-pixel localization of single molecules with an accuracy below
the diffraction limit is the basis of SMLM methods. ThunderSTORM supports
the following localization methods: calculation of the centroid of
the local neighborhood <cite class="ltx_cite">[<a href="#bib.bib9" title="QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ" class="ltx_ref">1</a>]</cite>, the radial symmetry
method <cite class="ltx_cite">[<a href="#bib.bib24" title="Rapid, accurate particle tracking by calculation of radial symmetry centers" class="ltx_ref">4</a>]</cite>, and fitting of point-spread function
models by (weighted) least-squares methods or by maximum likelihood
estimation <cite class="ltx_cite">[<a href="#bib.bib18" title="The Advanced Theory of Statistics" class="ltx_ref">2</a>, <a href="#bib.bib21" title="Optimized localization analysis for single-molecule tracking and super-resolution microscopy" class="ltx_ref">3</a>]</cite>. Users may also choose
not to use any of the methods, thereby using the approximate positions
of the molecules determined in the previous step. Note that the choice
of method for sub-pixel localization of molecules is independent of
the pre-processing methods described above.</p>
<ul class="ltx_itemize">
<li id="I1.ix1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize"><em class="ltx_emph">Input:</em></span> 
<div id="I1.ix1.p1" class="ltx_para">
<p class="ltx_p">A raw image <img id="I1.ix1.p1.m1" class="ltx_Math" style="vertical-align:-2px" src="mi/mi70.png" width="13" height="16" alt="I"> of size <img id="I1.ix1.p1.m2" class="ltx_Math" style="vertical-align:-3px" src="mi/mi73.png" width="52" height="15" alt="m\times n"> pixels and
a list of coordinates <img id="I1.ix1.p1.m3" class="ltx_Math" style="vertical-align:-10px" src="mi/mi72.png" width="104" height="32" alt="\left\{\left(\tilde{x}_{p},\tilde{y}_{p}\right)\right\}_{p=1}^{\tilde{P}}">
with approximate molecular positions.</p>
</div>
</li>
<li id="I1.ix2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize"><em class="ltx_emph">Output:</em></span> 
<div id="I1.ix2.p1" class="ltx_para">
<p class="ltx_p">A list of coordinates <img id="I1.ix2.p1.m1" class="ltx_Math" style="vertical-align:-10px" src="mi/mi71.png" width="104" height="33" alt="\left\{\left(\hat{x}_{p},\hat{y}_{p}\right)\right\}_{p=1}^{\hat{P}}">
with sub-pixel positions of the molecules.</p>
</div>
</li>
</ul>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<ul id="I2" class="ltx_itemize">
<li id="I2.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="../EmptyEstimator.html" title="" class="ltx_ref">No estimator</a></p>
</div>
</li>
<li id="I2.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="CenterOfMassEstimatorUI.html" title="" class="ltx_ref">Centroid of local neighborhood</a></p>
</div>
</li>
<li id="I2.i3" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i3.p1" class="ltx_para">
<p class="ltx_p"><a href="RadialSymmetryEstimatorUI.html" title="" class="ltx_ref">Radial symmetry</a></p>
</div>
</li>
<li id="I2.i4" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i4.p1" class="ltx_para">
<p class="ltx_p"><a href="PSF.html" title="" class="ltx_ref">Point-spread function (PSF)</a></p>
</div>
</li>
<li id="I2.i5" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i5.p1" class="ltx_para">
<p class="ltx_p"><a href="Fitting.html" title="" class="ltx_ref">Fitting point-spread function models</a></p>
</div>
</li>
<li id="I2.i6" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i6.p1" class="ltx_para">
<p class="ltx_p"><a href="FittingRegion.html" title="" class="ltx_ref">Definition of the fitting region</a></p>
</div>
</li>
<li id="I2.i7" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i7.p1" class="ltx_para">
<p class="ltx_p"><a href="LocalizationUncertainty.html" title="" class="ltx_ref">Localization uncertainty</a></p>
</div>
</li>
<li id="I2.i8" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I2.i8.p1" class="ltx_para">
<p class="ltx_p"><a href="CrowdedField.html" title="" class="ltx_ref">Multiple-emitter fitting analysis</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib9" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer and M. M. Mhlanga</span><span class="ltx_text ltx_bib_year">(2010)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">7</span> (<span class="ltx_text ltx_bib_number">5</span>), <span class="ltx_text ltx_bib_pages"> pp. 339–340</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1038/nmeth0510-339" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Sub-pixel 2D localization of molecules" class="ltx_ref"><span class="ltx_text ltx_ref_title">Sub-pixel 2D localization of molecules</span></a>.
</span>
</li>
<li id="bib.bib18" class="ltx_bibitem ltx_bib_book">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[2]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">M. Kendall and A. Stuart</span><span class="ltx_text ltx_bib_year">(1979)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">The Advanced Theory of Statistics</span>,
</span>
<span class="ltx_bibblock"> <span class="ltx_text ltx_bib_publisher">London: Charles Griffin</span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Sub-pixel 2D localization of molecules" class="ltx_ref"><span class="ltx_text ltx_ref_title">Sub-pixel 2D localization of molecules</span></a>.
</span>
</li>
<li id="bib.bib21" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[3]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">K. I. Mortensen, L. S. Churchman, J. A. Spudich and H. Flyvbjerg</span><span class="ltx_text ltx_bib_year">(2010)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Optimized localization analysis for single-molecule tracking and super-resolution microscopy</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">7</span> (<span class="ltx_text ltx_bib_number">5</span>), <span class="ltx_text ltx_bib_pages"> pp. 377–381</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/doi:10.1038/nmeth.1447" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Sub-pixel 2D localization of molecules" class="ltx_ref"><span class="ltx_text ltx_ref_title">Sub-pixel 2D localization of molecules</span></a>.
</span>
</li>
<li id="bib.bib24" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[4]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">R. Parthasarathy</span><span class="ltx_text ltx_bib_year">(2012)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Rapid, accurate particle tracking by calculation of radial symmetry centers</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">9</span> (<span class="ltx_text ltx_bib_number">7</span>), <span class="ltx_text ltx_bib_pages"> pp. 724–6</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1038/nmeth.2071" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Sub-pixel 2D localization of molecules" class="ltx_ref"><span class="ltx_text ltx_ref_title">Sub-pixel 2D localization of molecules</span></a>.
</span>
</li>
</ul>
</div>
</div>
</div>
<div class="ltx_page_footer">
<div class="ltx_page_logo">Generated  on Tue Jun  3 20:03:09 2014 by <a href="http://dlmf.nist.gov/LaTeXML/">LaTeXML <img src="" alt="[LOGO]"></a>
</div>
</div>
</div>
</body>
</html>
